An LMI based method for safety controller design

A common problem in industry is the issue of safety controllers. Usually there is a basic controller that works well for normal conditions, but when certain state variables get too large we need to switch to a safety controller in order to get the state back to a normal level. The design of the safety controller such that it works well together with the basic controller is the topic of the paper. In practice, the design is often done in an ad hoc manner. The paper describes an approach to extending a given static output feedback control law with a safety controller. The safety controller is activated when the state gets close to the forbidden region in state space. It pushes the state to a safe distance from the forbidden region within a maximum prescribed time despite disturbances. It does this with a prescribed bound on the input and in a manner that guarantees stability of the overall system. The switching between the two controllers takes place through hysteresis, this helps to avoid chattering. The method is based on LMIs which ensures scalability to large systems. However, the LMI approach imposes some conservatism on the results. Also, the method is as at present limited to systems with a relative degree one from the input to a specific output of the system